Paraconsistency and beyond: A new approach to inconsistency handling

Abstract

The expressive power of positive logic programs is enhanced by explicit negation by providing a natural and unambiguous way to assert negated information. But by this, we are faced with the problem of dealing with contradictions in the database. The ECSQ (for ‘ex contradictione sequitir quodlibet’) approach of classical logic, by which everything follows from a contradiction, thus resulting in the collapsing (or trivialization) of the system is certainly not a pragmatic approach towards handling inconsistency. We propose an inconsistency handling concept — explicit paraconsistency, formalized as Approach C, which is close in spirit to ‘paraconsistent’ approaches known from the logicophilosophical literature on non-classical logics handling inconsistency. Furthermore, our approach goes beyond the paraconsistent horizon i.e. allowing nontrivial reasoning in presence of inconsistency. We allow reasoning from inconsistent information, keep track of conclusions inferred from inconsistent premises and propagate a new horizon of reasoning involving elements ‘affected’ by inconsistency. This we call reasoning beyond paraconsistency and formalize as Approach C _d.